Solid cover for deck floor?

I want to cover my upper deck floor so it won't drip down on my lower deck. The lower deck is practically unuseable because of all the water, dirt, rain and snow dripping from the upper deck. Is it possible to cover the upper deck floor with something to prevent this or will I have to replace the redwood planks with a new material?

You can cover the upper deck with pressure-treated plywood and maybe indoor/outdoor carpeting over that, but I think that it would tend to shorten the life of your redwood planking by holding more moisture. I believe that I would replace the redwood planking with pressure-treated decking for a long-term solution.